After a couple of hours of looking through everything I have, I see nothing that explicitly says that communion has to be given by hand or that it cannot be given by a dispenser like those above. This is possibly due to the fact that in some Catholic Churches of other rites, it is not given by hand.

Like so.

Next question: Why does this go against our sensibilities then? Why are we so completely bugged by a Jesus PEZ?

The first thought I have is directly related to the phrase "Jesus PEZ." It's disrespectful to take communion the same way we take candy. Communion is unlike anything else we eat and it shouldn't be consumed in an ordinary way.

These dispensers are silver and gold, though. And isn't it important to take communion in the right frame of mind? Can't it be reverent regardless of the trappings?

The old-school definition of sacrament is: an outward sign of an inward grace. So the outer trappings really do matter.

Simply put, we take actions and outer trappings very seriously, especially when it comes to our Sacraments. The inner life affects the outer actions. The outer actions certainly affect the inner disposition.